D&D 5E - Defensive Duelist feat and dual-wielding
Rules as written; one weapon or two, as long as one is a finesse weapon you should be golden.The one handed style we're most familiar with today, thanks to fencing, developed in the 19th Century, based largely on the swordplay of the 18th Century, considerably postdates the time periods D&D is usually intended to emulate. Until double time fencing came into vogue (and the rapier evolved into the smallsword), one almost always wanted an off-hand weapon of some time, or cloak or hat, if a buckler or poniard was not available.
One can single time with an open off-hand, but it's not ideal.
If we're talking about formal duels, those were fought with whatever style and in whatever manner was agreed upon by the participants (variations depending on place and period), much like judicial combats of an earlier period. My understanding is because it was possible that one would have to defend themselves with naught but a single sword, it became common to train that way, and as such, the lengths of rapiers gradually shortened and lightened, until we finally come to the bit of man jewelry known as the smallsword.
But technically, a duel is just a formal combat between two participants. You could have a duel between two dudes with two-handed longswords as easily as you could with rapiers.
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